Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

The RatSLAM project : robot spatial navigation

Rats are superior to the most advanced robots when it comes to creating and exploiting spatial representations. A wild rat can have a foraging range of hundreds of meters, possibly kilometers, and yet the rodent can unerringly return to its home after each foraging mission, and return to profitable foraging locations at a later date (Davis, et al., 1948). The rat runs through undergrowth and pipes with few distal landmarks, along paths where the visual, textural, and olfactory appearance constantly change (Hardy and Taylor, 1980; Recht, 1988). Despite these challenges the rat builds, maintains, and exploits internal representations of large areas of the real world throughout its two to three year lifetime. While algorithms exist that allow robots to build maps, the questions of how to maintain those maps and how to handle change in appearance over time remain open. The robotic approach to map building has been dominated by algorithms that optimise the geometry of the map based on measurements of distances to features. In a robotic approach, measurements of distance to features are taken with range-measuring devices such as laser range finders or ultrasound sensors, and in some cases estimates of depth from visual information. The features are incorporated into the map based on previous readings of other features in view and estimates of self-motion. The algorithms explicitly model the uncertainty in measurements of range and the measurement of self-motion, and use probability theory to find optimal solutions for the geometric configuration of the map features (Dissanayake, et al., 2001; Thrun and Leonard, 2008). Some of the results from the application of these algorithms have been impressive, ranging from three-dimensional maps of large urban strucutures (Thrun and Montemerlo, 2006) to natural environments (Montemerlo, et al., 2003).

Lingodroids : studies in spatial cognition and language

The Lingodroids are a pair of mobile robots that evolve a language for places and relationships between places (based on distance and direction). Each robot in these studies has its own understanding of the layout of the world, based on its unique experiences and exploration of the environment. Despite having different internal representations of the world, the robots are able to develop a common lexicon for places, and then use simple sentences to explain and understand relationships between places even places that they could not physically experience, such as areas behind closed doors. By learning the language, the robots are able to develop representations for places that are inaccessible to them, and later, when the doors are opened, use those representations to perform goal-directed behavior.

A Bayesian analysis of an agricultural field trial with three spatial dimensions

Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.

A spatial collision avoidance strategy for UAVs in a non-cooperative environment

This paper presents a feasible spatial collision avoidance approach for fixed-wing unmanned aerial vehicles (UAVs). The proposed strategy aims to achieve the desired relative bearing in the horizontal plane and relative elevation in the vertical plane so that the host aircraft is able to avoid collision with the intruder aircraft in 3D. The host aircraft will follow a desired trajectory in the collision avoidance course and resume the pre-arranged trajectory after collision is avoided. The approaching stopping condition is determined for the host aircraft to trigger an evasion maneuver to avoid collision in terms of measured heading. A switching controller is designed to achieve the spatial collision avoidance strategy. Simulation results demonstrate that the proposed approach can effectively avoid spatial collision, making it suitable for integration into flight control systems of UAVs.

Environmental factors controlling temporal and spatial variability in the soil-atmosphere exchange of CO2, CH4 and N2O from an Australian subtropical rainforest

The temporal variations in CO2, CH4 and N2O fluxes were measured over two consecutive years from February 2007 to March 2009 from a subtropical rainforest in south-eastern Queensland, Australia, using an automated sampling system. A concurrent study using an additional 30 manual chambers examined the spatial variability of emissions distributed across three nearby remnant rainforest sites with similar vegetation and climatic conditions. Interannual variation in fluxes of all gases over the 2 years was minimal, despite large discrepancies in rainfall, whereas a pronounced seasonal variation could only be observed for CO2 fluxes. High infiltration, drainage and subsequent high soil aeration under the rainforest limited N2O loss while promoting substantial CH4 uptake. The average annual N2O loss of 0.5 ± 0.1 kg N2O-N ha−1 over the 2-year measurement period was at the lower end of reported fluxes from rainforest soils. The rainforest soil functioned as a sink for atmospheric CH4 throughout the entire 2-year period, despite periods of substantial rainfall. A clear linear correlation between soil moisture and CH4 uptake was found. Rates of uptake ranged from greater than 15 g CH4-C ha−1 day−1 during extended dry periods to less than 2–5 g CH4-C ha−1 day−1 when soil water content was high. The calculated annual CH4 uptake at the site was 3.65 kg CH4-C ha−1 yr−1. This is amongst the highest reported for rainforest systems, reiterating the ability of aerated subtropical rainforests to act as substantial sinks of CH4. The spatial study showed N2O fluxes almost eight times higher, and CH4 uptake reduced by over one-third, as clay content of the rainforest soil increased from 12% to more than 23%. This demonstrates that for some rainforest ecosystems, soil texture and related water infiltration and drainage capacity constraints may play a more important role in controlling fluxes than either vegetation or seasonal variability

Spatial and temporal clusters of Barmah Forest virus disease in Queensland, Australia

Objective To identify the spatial and temporal clusters of Barmah Forest virus (BFV) disease in Queensland in Australia, using geographical information systems (GIS) and spatial scan statistic (SaTScan). Methods We obtained BFV disease cases, population and statistical local areas boundary data from Queensland Health and Australian Bureau of Statistics respectively during 1992-2008 for Queensland. A retrospective Poisson-based analysis using SaTScan software and method was conducted in order to identify both purely spatial and space-time BFV disease high-rate clusters. A spatial cluster size of a proportion of the population and a 200km circle radius and varying time windows from 1 month to 12 months were chosen (for the space-time analysis). Results The spatial scan statistic detected a most likely significant purely spatial cluster (including 23 SLAs) and a most likely significant space-time cluster (including 24 SLAs) in approximately the same location. Significant secondary clusters were also identified from both the analyses in several locations. Conclusions This study provides evidence of the existence of statistically significant BFV disease clusters in Queensland, Australia. The study also demonstrated the relevance and applicability of SaTScan in analysing on-going surveillance data to identify clusters to facilitate the development of effective BFV disease prevention and control strategies in Queensland, Australia.

Spatial inequalities in colorectal and breast cancer survival : premature deaths and associated factors

This study examines the influence of cancer stage, distance to treatment facilities and area disadvantage on breast and colorectal cancer spatial survival inequalities. We also estimate the number of premature deaths after adjusting for cancer stage to quantify the impact of spatial survival inequalities. Population-based descriptive study of residents aged <90 years in Queensland, Australia diagnosed with primary invasive breast (25,202 females) or colorectal (14,690 males, 11,700 females) cancers during 1996-2007. Bayesian hierarchical models explored relative survival inequalities across 478 regions. Cancer stage and disadvantage explained the spatial inequalities in breast cancer survival, however spatial inequalities in colorectal cancer survival persisted after adjustment. Of the 6,019 colorectal cancer deaths within 5 years of diagnosis, 470 (8%) were associated with spatial inequalities in non-diagnostic factors, i.e. factors beyond cancer stage at diagnosis. For breast cancers, of 2,412 deaths, 170 (7%) were related to spatial inequalities in non-diagnostic factors. Quantifying premature deaths can increase incentive for action to reduce these spatial inequalities.

The spatial distribution of rodent damage in Australian macadamia (Macadamia integrifolia) orchards

The Black Rat (Rattus rattus), a global pest within the macadamia production industry, causes up to 30% crop damage in Australian orchards. During early stages of production in Australia, research demonstrated the importance of non crop adjacent habitats as significant in affecting the patterns of crop damage seen throughout orchards. Where once rodent damage was limited to the outside edges of orchard blocks, growers are now reporting finding crop damage throughout entire orchards. This study therefore aims to explore the spatial patterns of rodent distribution and damage now occurring in Australian macadamia orchards. We show that rodent damage and rodent distribution in these newer production regions differ from that shown in previous Australian research. Previous Australian research has shown damage patterns which were associated with the edges of orchard blocks however this study demonstrates a more widespread damage distribution. In the current study there is no relationship between rodent damage and the orchard edge. Arboreal rodent nests were identified within these newer orchard systems, suggesting rodents are residing within the tree component of the orchard system and not dependent on adjacent non-crop habitat for shelter. Results from this study confirm that rodents have modified their nesting and foraging behaviour in newer orchards systems in Australia. We suggest that this is a response of increased and prolonged availability of macadamia nuts in newer production regions enabling populations to be maintained throughout the year. Management strategies will require modification if control is to be achieved.

A hybrid model for studying spatial aspects of infectious diseases

We consider a hybrid model, created by coupling a continuum and an agent-based model of infectious disease. The framework of the hybrid model provides a mechanism to study the spread of infection at both the individual and population levels. This approach captures the stochastic spatial heterogeneity at the individual level, which is directly related to deterministic population level properties. This facilitates the study of spatial aspects of the epidemic process. A spatial analysis, involving counting the number of infectious agents in equally sized bins, reveals when the spatial domain is nonhomogeneous.

Environmental and economic evaluation of N fertilizer rates in a maize crop in Italy : a spatial and temporal analysis using crop models

Crop simulation models have the potential to assess the risk associated with the selection of a specific N fertilizer rate, by integrating the effects of soil-crop interactions on crop growth under different pedo-climatic and management conditions. The objective of this study was to simulate the environmental and economic impact (nitrate leaching and N2O emissions) of a spatially variable N fertilizer application in an irrigated maize field in Italy. The validated SALUS model was run with 5 nitrogen rates scenarios, 50, 100, 150, 200, and 250 kg N ha−1, with the latter being the N fertilization adopted by the farmer. The long-term (25 years) simulations were performed on two previously identified spatially and temporally stable zones, a high yielding and low yielding zone. The simulation results showed that N fertilizer rate can be reduced without affecting yield and net return. The marginal net return was on average higher for the high yield zone, with values ranging from 1550 to 2650 € ha−1 for the 200 N and 1485 to 2875 € ha−1 for the 250 N. N leaching varied between 16.4 and 19.3 kg N ha−1 for the 200 N and the 250 N in the high yield zone. In the low yield zone, the 250 N had a significantly higher N leaching. N2O emissions varied between 0.28 kg N2O ha−1 for the 50 kg N ha−1 rate to a maximum of 1.41 kg N2O ha−1 for the 250 kg N ha−1 rate.

Airborne particle concentrations at schools measured at different spatial scales

Potential adverse effects on children health may result from school exposure to airborne particles. To address this issue, measurements in terms of particle number concentration, particle size distribution and black carbon (BC) concentrations were performed in three school buildings in Cassino (Italy) and its suburbs, outside and inside of the classrooms during normal occupancy and use. Additional time resolved information was gathered on ventilation condition, classroom activity, and traffic count data around the schools were obtained using a video camera. Across the three investigated school buildings, the outdoor and indoor particle number concentration monitored down to 4 nm and up to 3 m ranged from 2.8×104 part cm-3 to 4.7×104 part cm-3 and from 2.0×104 part cm-3 to 3.5×104 part cm-3, respectively. The total particle concentrations were usually higher outdoors than indoors, because no indoor sources were detected. I/O measured was less than 1 (varying in a relatively narrow range from 0.63 to 0.74), however one school exhibited indoor concentrations higher than outdoor during the morning rush hours. Particle size distribution at the outdoor site showed high particle concentrations in different size ranges, varying during the day; in relation to the starting and finishing of school time two modes were found. BC concentrations were 5 times higher at the urban school compared with the suburban and suburban-to-urban differences were larger than the relative differences of ultrafine particle concentrations.